B-BIMORPHISMS

Abstract

Let $X$ be an Archimedean vector lattice and it has a separating order dual $X^{\sim}$. By $(X^{\sim})^{\sim}_{n}$ we denote the order continuous bidual of $X$. In this paper, we define a b-bimorphism of $X$ and we extend it to the order continuous bidual of $X$.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 32
Issue: 1
Year: 2019

DOI: 10.12732/ijam.v32i1.4

Download Section



Download the full text of article from here.

You will need Adobe Acrobat reader. For more information and free download of the reader, please follow this link.

References

  1. [1] C.D. Aliprantis, O. Burkinshw, Positive Operators, Academic Press, New York (1985).
  2. [2] R. Arens, The adjoint of bilinear operations, Proc. Amer. Math. Soc., 2 (1951), 839-848.
  3. [3] S.J. Bernau, C.B. Huijsmans, The order bidual of almost f-algebras and d-algebras, Trans. Amer. Math. Soc., 347 (1986), 4259-4275.
  4. [4] K. Boulabair, W. Brahmi, Multiplicative structure of biorthomorphisms and embedding of orthomorphisms, Indagationes Math., 27 (2016), 786-798.
  5. [5] G. Buskes, Jr.R. Page, R. Yilmaz, A note on biorthomorphisms. Vector Measures, Integration and related topics, In: Operator Theory, Advances and Applications, 201 (2009), 99-107.
  6. [6] C.B. Huijsmans, B. de Pagter, The order bidual of lattice ordered algebras, J. Funct Anal., 59 (1984), 41-64.
  7. [7] P. Meyer-Nieberg, Banach Lattices, Springer, Berlin (1991).
  8. [8] M.A. Toumi, The triadjoint of an orthosymmetric bimorphism, Czeshoslovak Math. J., 60, No 135 (2010), 85-94.
  9. [9] B. Turan, M. Aslantas, Archimedean l-algebras with multiplication closed bands, Indagationes Math., 25, No 2 (2014), 588-595.
  10. [10] R. Yilmaz, The Arens triadjoints of some bilinear maps, Filomat, 28, No 5 (2014), 963-979.
  11. [11] R. Yilmaz, A note on bilinear maps on vector lattices, New Trends Math. Sci., 5, No 3 (2017), 168-174.